Black hole singularity resolution via the modified Raychaudhuri equation in loop quantum gravity

Abstract

We derive loop quantum gravity corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole and near the classical singularity. We show that the resulting effective equation implies defocusing of geodesics due to the appearance of repulsive terms. This prevents the formation of conjugate points, renders the singularity theorems inapplicable, and leads to the resolution of the singularity for this spacetime.

arXiv comment28 pages, 10 figures, v2: additional citations added, v3: figure 5 added, few modifications to the text and stronger defocusing results presented

References in corpus (61)

• Quantum Nature of the Big Bang
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Quantum geometry and the Schwarzschild singularity
• Quantum gravity, shadow states, and quantum mechanics
• Loop quantum black hole
• Quantum Extension of the Kruskal Space-time
• Loop Quantum Dynamics of the Schwarzschild Interior
• Loop quantization of the Schwarzschild black hole
• Space-Time Structure of Loop Quantum Black Hole
• Polymer Quantum Mechanics and its Continuum Limit
• Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's Self-Dual Representation
• Black holes in loop quantum gravity: the complete space-time
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• Loop quantization of the Schwarzschild interior revisited
• From black holes to white holes: a quantum gravitational, symmetric bounce
• Spherically Symmetric Quantum Geometry: Hamiltonian Constraint
• Phenomenological loop quantum geometry of the Schwarzschild black hole
• Effective loop quantum gravity framework for vacuum spherically symmetric space-times
• Effective line elements and black-hole models in canonical (loop) quantum gravity
• Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole
• Loop quantization of spherically symmetric midi-superspaces
• Self-dual Black Holes in LQG: Theory and Phenomenology
• Spherically symmetric loop quantum gravity: analysis of improved dynamics
• Polymer Schwarzschild black hole: An effective metric
• Loop quantization of spherically symmetric midi-superspaces : the interior problem
• Quantum gravity predictions for black hole interior geometry
• Black hole collapse and bounce in effective loop quantum gravity
• Quantum resolution of black hole singularities
• Quantum Raychaudhuri equation
• Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity
• Phenomenological dynamics of loop quantum cosmology in Kantowski-Sachs spacetime
• On effective loop quantum geometry of Schwarzschild interior
• Kantowski-Sachs spacetime in loop quantum cosmology: bounds on expansion and shear scalars and the viability of quantization
• Loop quantum Schwarzschild interior and black hole remnant
• Quantum gravitational collapse: non-singularity and non-locality
• Non-singular black holes and the Limiting Curvature Mechanism: A Hamiltonian perspective
• Bouncing compact objects I: Quantum extension of the Oppenheimer-Snyder collapse
• Spherically symmetric canonical quantum gravity
• Non-local (but also non-singular) physics at the last stages of gravitational collapse
• Schrodinger formalism, black hole horizons and singularity behavior
• Quantum evolution of black hole initial data sets: Foundations
• Signature change in 2-dimensional black-hole models of loop quantum gravity
• Bouncing compact objects. Part II: Effective theory of a pulsating Planck star
• Signature change in loop quantum gravity: General midisuperspace models and dilaton gravity
• Towards the Raychaudhuri Equation Beyond General Relativity
• Propagators in Polymer Quantum Mechanics
• Modified general relativity as a model for quantum gravitational collapse
• Asymptotically de Sitter Universe inside a Schwarzschild black hole
• Stability of the Schwarzschild Interior in Loop Quantum Gravity
• Path integral polymer propagator of relativistic and non-relativistic particles
• Quantum scalar field in quantum gravity: the vacuum in the spherically symmetric case
• Polymer quantization and the saddle point approximation of partition functions
• Polymer Quantization of a Self-Gravitating Thin Shell
• Quantum Hamiltonian for gravitational collapse
• Effective dynamics of the Schwarzschild black hole interior with inverse triad corrections
• Constraints and Horizons for de Sitter with Extra Dimensions
• Callan-Giddings-Harvey-Strominger vacuum in loop quantum gravity and singularity resolution
• Dilaton Gravity, Poisson Sigma Models and Loop Quantum Gravity
• New variables for 1+1 dimensional gravity
• Constraint Lie algebra and local physical Hamiltonian for a generic 2D dilatonic model
• Quantum scalar field in quantum gravity: the propagator and Lorentz invariance in the spherically symmetric case

Cited by in corpus (29)

• Testing loop quantum gravity from observational consequences of non-singular rotating black holes
• Tests of Loop Quantum Gravity from the Event Horizon Telescope Results of Sgr A${}^{\ast }$
• On the fate of quantum black holes
• Gravitational lensing by a black hole in effective loop quantum gravity
• Destroying the event horizon of a nonsingular rotating quantum-corrected black hole
• Deformed algebra and the effective dynamics of the interior of black holes
• Effective Quantum Dust Collapse via Surface Matching
• Effective GUP-modified Raychaudhuri equation and black hole singularity: four models
• The Raychaudhuri equation for a quantized timelike geodesic congruence
• Loop Quantum Gravity motivated multihorizon rotating black holes
• Finite-distance gravitational deflection of massive particles by a rotating black hole in loop quantum gravity
• Annihilation-to-nothing: DeWitt boundary condition inside a black hole
• Probing a polymerized black hole with the frequency shifts of photons
• Black hole interior quantization: a minimal uncertainty approach
• Ascribing quantum system to Schwarzschild spacetime with naked singularity
• Graviton noise on tidal forces and geodesic congruences
• A generalized uncertainty-inspired quantum black hole
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Loop effective model for Schwarzschild black hole interior: a modified $\bar{\mu }$ dynamics
• On the Possible Spacetime Structures of Rotating Loop Quantum Black Holes
• Black Hole singularity and its possible mitigations: Reformulation of Penrose Singularity theorem using null Raychaudhuri matrix
• Trouble with geodesics in black-to-white hole bouncing scenarios
• Quantum geometry and black holes
• Quantum Black Hole as a Harmonic Oscillator from the Perspective of the Minimum Uncertainty Approach
• Quantum Groups and Polymer Quantum Mechanics
• An analytic model for a total process of gravitational collapse: From star to Schwarzschild black hole
• Probing the interior of the Schwarzschild black hole using congruences: LQG vs. GUP
• Singularity avoidance from path integral
• Report on the session Loop Quantum Gravity: Cosmology and Black Holes of the 16th Marcel Grossmann Meeting